A line of charge (with charge per unit length given by λ)extends from (0,0,0) along the x axis to infinity. Answer thefollowing 2 questions about the electric field atthe point (x,y,z) = (0,a,0).

1. A correct integral expression for the ycomponent of the electric field at this point is given bywhich of the following? In each case the integral has limits 0 and∞.
   1. λ/(4πε₀)∫dx a/(a² +x²)^3/2 k
   2. λ/(4πε₀)∫dx a/(a² +x²)^3/2 j
   3. λ/(4πε₀)∫dx a/(a² + x²)^{   Â} j
   4. λ/(4πε₀)∫dx a/(a² +x²)^1/2k
   5. none of a-d   

                                                                   

1. What is the y component of the electric field at this point?Hint: remember (or calculate using Gauss’s law) theelectric field a distance a from an infinite wire and think of asymmetry argument that allows you to answer the question without amore complicated calculation.

1. E_y = λ/(4Ï€aε₀)j
2. E_y = λ/(2Ï€aε₀)j
3. E_y = λ/(4Ï€aε₀)k
4. E_y = λ/(2Ï€aε₀)i    
5. none ofa-d                                                                            

1. Which of the following is(are) true about acharged particle in a uniform, static (time-independent) magneticfield?
   1. The magnitude of the magnetic force on the particle dependsonly on the charge, the magnetic field and physical constants.
   2. The magnitude of the magnetic force on the particle depends onthe direction of motion of the particle
   3. The work done on the particle by the magnetic force depends onthe velocity of the particle.
   4. If the particle is moving, the magnetic force on the particlecannot be zero.
   5. More than one of a-d